Guess the Random Number

A lottery at Youngkwa Day awards prizes to members who solved many problems during one semester.

Each member gets a weight that raises their chance of winning. If a member solved $p$ problems, their weight is $p$.

There are $N$ members who solved at least one problem this semester. They are numbered from $1$ to $N$.

The lottery picks $M(1 \leq M \leq N)$ winners out of the $N$ members. It starts with $i=1$ and runs as follows.

1. Going through members $1$ to $N$ in order, add each member's ticket to the list $W$ as many times as their weight. For example, if there are 3 members with weights $2,\ 1,\ 3$, then $W = [T_1, T_1, T_2, T_3, T_3, T_3]$. ($T_k$ is the ticket of member $k$.)
2. Pick one integer from $1$ to $|W|$ at random and call it $X_i$.
3. Select the $X_i$-th ticket from the front of $W$ to pick one winner.
4. Remove all tickets of the member who just won from $W$.
5. If $i \neq M$, increase $i$ by $1$ and go back to step 2. Otherwise, end the lottery.

The winners' numbers are given in the order they were drawn. Guess which random numbers were drawn, in order.

The first line contains $N$ and $M$, separated by a space. $(1 \leq N \leq 500\,000; 1 \leq M \leq N)$

The second line contains the weight $p$ of each member, separated by spaces. There are $N$ values. $(1 \leq p \leq 1\,000)$

The third line contains the member numbers $k$ of the winners, in the order they were drawn, separated by spaces. There are $M$ values. $(1 \leq k \leq N)$

All input values are integers.

Print the sequence $X$ of random numbers drawn during the lottery, separated by spaces.

If more than one sequence is possible, print any one of them.